Where particulate materials such as powdered or granular materials are processed, stored, packaged or the like, it is often desired to monitor the particle size of the particulates.
It is known that the rate of flow of particulate material through an orifice is determined by a number of factors including the bulk density of the material, the size of the orifice or slot, and the size of the particles. Various mathematical formulae have been put forward to describe the relationship between the parameters that affect flow rate. An equation to describe the flow rate of particles through a circular horizontal orifice in the bottom of a flat bottomed container was published by Beverloo, Leniger, and van de Velde, in the Journal, Chemical Engineering Science, volume 15, 1961. This formula is EQU m.sub.hf =Keg.sup.1/2 (D-k.sub.h d).sup.5/2 ( 1)
where m.sub.hf is the flow rate through a horizontal orifice in a container with a flat bottom, K is a constant found by Beverloo et al to be 0.58 for agricultural seeds and sand grains and similar but which may show some small variation from material to material, which may be determined by experimentation, e is the bulk density of the material; g is acceleration due to gravity; D is the diameter of the orifice; d is the characteristic diameter of the particles; and k.sub.h is a parameter that is related to particle size.
When the bottom of the container is not flat, the flow rate can be described by similar formulae. For example, N P Cheremisinoff and P N Cheremisinoff writing in "The Encyclopedia of Fluid Mechanics", volume 4 in "Solids and Gas-Solids Flows", which is published by Gulf Publishing Company, Houston, Tex., U.S.A., have given a formula for the flow rate through a container with a conical bottom; the formula follows the approach taken earlier by Rose and Tanaka who published their work in Engineer, volume 208, 1959. Rose and Tanaka proposed that the effect of a conical bottom on a container can be accounted for by a correction factor (tan .alpha. tan .theta.).sup.-0.35, where .theta. is the angle of inclination of the hopper wall to the vertical, and .alpha. is the angle of repose of the granular material. N P Cheremisinoff and P N Cheremisinoff stated that the correction factor suggested by Rose and Tanaka can be applied to equation 1 giving a formula for the flow rate m.sub.hc of a granular solid through a circular opening in the bottom of a container with a conical bottom: EQU m.sub.hc =Keg.sup.1/2 (D-k.sub.h d).sup.5/2 (tan .alpha. tan .theta.).sup.-0.35 ( 2)
(.pi./2-.alpha.) should be larger than .theta..
It will be appreciated by those skilled in the art that there some restrictions on the use of this formula, such as when the ratio of the diameter of the container to the diameter of the orifice is small for example, and proper care and caution should be taken when the formula is used.
The effect of particle size on flow rate from containers with conical bottoms is similar to the effect on flow rate from containers with flat bottoms.